Shares of Time Inc. continued to lose value Monday on the second day of trading since the giant media company announced that it will take on a massive new debt to acquire Warner Communications for $14 billion.

Time's stock dropped $5.625 to close at $156.875 per share, as about 2 million shares traded on the New York Stock Exchange.

The downward drift was slowed by traders' speculation that a Delaware court challenge may yet force Time to accept a hostile takeover bid from Paramount Communications that was made two weeks ago.

The legal issues are expected to be thrashed out on July 11 in a Delaware court hearing, just six days before the expiration of Time's friendly cash offer for half of Warner's shares. Time has promised to offer a combination of cash and stock or debt securities worth $70 for each remaining Warner share, but the formula has not yet been announced.

Determined to Close Deal

Wall Street's skepticism about the deal is reflected in the fact that Warner's shares are still not trading near the $70 price offered by Time. Warner stock closed at $59.625, up 37.5 cents on a volume of nearly 4.5 million shares, making it the most active issue on the New York Stock Exchange. (Time's trading volume ranked seventh for the day.)

Meanwhile, advisers to Paramount spent most of the day conferring about that entertainment company's next move. The company is expected to soon amend an earlier complaint to the Delaware court to update its challenge to Time's anti-takeover defenses.

Failing a court order to halt their merger, Time and Warner are determined to close their deal as quickly as possible.

"We intend to close (the Time-Warner offer) on July 17," Warner spokesman Geoffrey W. Holmes said. "We have gotten the necessary licenses to do this."

In addition to clearing federal antitrust reviews, Time and Warner have devoted 3 1/2 months to the task of arranging transfer of certain cable television licenses at various governmental levels. Holmes, like a number of officials at Warner and Time, questioned Paramount's ability to secure such approvals quickly enough to consummate its tender offer--now set to expire July 5.

Paramount's shares, meanwhile, gained $2.375 to close at $60.50, with nearly 2.3 million shares changing hands on speculative talk that Paramount itself might become a takeover target.

While Time's rejection of Paramount's cash offer has clearly left some Time shareholders steaming, other big holders view the drama with unresolved feelings.

A number of Time's biggest shareholders are professional investors who hold big blocks of all three companies. Others aren't sure how they feel because they believe that the battle is far from decided.

"We're watching it and not taking any action; there are still a lot more cards to be played," said Dale Hanson, chief executive of California Public Employees Retirement System in Sacramento, which holds blocks of stock in all three companies.

Holding Out Hope

Theodore Fitilis, an investment analyst and senior vice president of Alliance Capital Management in New York, said he has spent a lot of time trying to fathom the contest and found it "very difficult to unscramble."

But even if the outcome is difficult to see, Fitilis believes that the stocks of the surviving firms will be higher than they were before the takeover moves began. "No matter who buys what, I think probably all three stocks will benefit from this," he said.

He also has scenario he considers ideal: Time buys Warner, and then both are acquired by Paramount.

Some other big shareholders are holding out hope that Time will make some move to make the deal more palatable to its shareholders. Eugene Sit, principal in Sit Investment Associates in Minneapolis, says he supports the Time bid for Warner, believing managements' arguments that the merged company will be poised for expansion.

Still, "Time's got to do something for the shareholders, and I'm sure they will," Sit said.

Separately Monday, Time's tender offer documents made public for the first time certain financial projections for Warner. According to data assembled in February, Warner estimated that its operating income for 1990 would leap to $1 billion, up from $731 million projected in 1989, and $246 million in the company's 1988 results, which were restated to include Warner's recent acquisition of Lorimar Telepictures.

Kathryn Harris reported from Los Angeles and Paul Richter reported from New York.